Hair too rigid unable to get rid of right angle structure
You might want to add more control points to the hair particles. The goal is the add some extra control points near the scalp/head so hair can bend nicely there.

To do so, make sure Selection Mode: Point is active to see the points. Select all roots by using the menu. Then select the next points via the menu (Select → Select More or hit Ctrl + NumPad +). Now you add another control point for each hair particle with Particle → Subdivide.
Extend the selection before subdivision or repeat the steps when you need more control points. The selection can also help you to comb or puff only the parts of the hair strands you want.
To see the effect you need to increase the number of path steps for the hair. There are 3 settings for this. One in the tool options for the Particle Edit mode. Then for the final Render and one more for the Viewport Display. The default values are 2 or 3, often too low to bend the hair properly.